sorcsd2by1.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

sorcsd2by1.f  

SYNOPSIS


 

Functions/Subroutines


subroutine sorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO)
SORCSD2BY1  

Function/Subroutine Documentation

 

subroutine sorcsd2by1 (character JOBU1, character JOBU2, character JOBV1T, integer M, integer P, integer Q, real, dimension(ldx11,*) X11, integer LDX11, real, dimension(ldx21,*) X21, integer LDX21, real, dimension(*) THETA, real, dimension(ldu1,*) U1, integer LDU1, real, dimension(ldu2,*) U2, integer LDU2, real, dimension(ldv1t,*) V1T, integer LDV1T, real, dimension(*) WORK, integer LWORK, integer, dimension(*) IWORK, integer INFO)

SORCSD2BY1

Purpose:

 SORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
 orthonormal columns that has been partitioned into a 2-by-1 block
 structure:

                                [  I1 0  0 ]
                                [  0  C  0 ]
          [ X11 ]   [ U1 |    ] [  0  0  0 ]
      X = [-----] = [---------] [----------] V1**T .
          [ X21 ]   [    | U2 ] [  0  0  0 ]
                                [  0  S  0 ]
                                [  0  0  I2]

 X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
 (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
 nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
 R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a
 K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).


 

Parameters:

JOBU1

          JOBU1 is CHARACTER
          = 'Y':      U1 is computed;
          otherwise:  U1 is not computed.


JOBU2

          JOBU2 is CHARACTER
          = 'Y':      U2 is computed;
          otherwise:  U2 is not computed.


JOBV1T

          JOBV1T is CHARACTER
          = 'Y':      V1T is computed;
          otherwise:  V1T is not computed.


M

          M is INTEGER
          The number of rows in X.


P

          P is INTEGER
          The number of rows in X11. 0 <= P <= M.


Q

          Q is INTEGER
          The number of columns in X11 and X21. 0 <= Q <= M.


X11

          X11 is REAL array, dimension (LDX11,Q)
          On entry, part of the orthogonal matrix whose CSD is desired.


LDX11

          LDX11 is INTEGER
          The leading dimension of X11. LDX11 >= MAX(1,P).


X21

          X21 is REAL array, dimension (LDX21,Q)
          On entry, part of the orthogonal matrix whose CSD is desired.


LDX21

          LDX21 is INTEGER
           The leading dimension of X21. LDX21 >= MAX(1,M-P).


THETA

          THETA is REAL array, dimension (R), in which R =
          MIN(P,M-P,Q,M-Q).
          C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
          S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).


U1

          U1 is REAL array, dimension (P)
          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.


LDU1

          LDU1 is INTEGER
          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
          MAX(1,P).


U2

          U2 is REAL array, dimension (M-P)
          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
          matrix U2.


LDU2

          LDU2 is INTEGER
          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
          MAX(1,M-P).


V1T

          V1T is REAL array, dimension (Q)
          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
          matrix V1**T.


LDV1T

          LDV1T is INTEGER
          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
          MAX(1,Q).


WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
          If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
          ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
          define the matrix in intermediate bidiagonal-block form
          remaining after nonconvergence. INFO specifies the number
          of nonzero PHI's.


LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the work array, and no error
          message related to LWORK is issued by XERBLA.


IWORK

          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))


INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  SBBCSD did not converge. See the description of WORK
                above for details.


 

References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

July 2012

Definition at line 235 of file sorcsd2by1.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine sorcsd2by1 (character JOBU1, character JOBU2, character JOBV1T, integer M, integer P, integer Q, real, dimension(ldx11,*) X11, integer LDX11, real, dimension(ldx21,*) X21, integer LDX21, real, dimension(*) THETA, real, dimension(ldu1,*) U1, integer LDU1, real, dimension(ldu2,*) U2, integer LDU2, real, dimension(ldv1t,*) V1T, integer LDV1T, real, dimension(*) WORK, integer LWORK, integer, dimension(*) IWORK, integer INFO)
Author